Question

system a
line 1: $y = - \frac{1}{2}x - 2$
line 2: $x + 2y = - 4$
this system of equations is:
consistent independent
consistent dependent
inconsistent
this means the system has:
a unique solution
solution: (, )
infinitely many solutions
no solution

Explanation:

Step1: Rewrite Line 2 in slope - intercept form

Starting with \(x + 2y=-4\).
Subtract \(x\) from both sides: \(2y=-x - 4\).
Divide by \(2\): \(y=-\frac{1}{2}x-2\).

Step2: Compare the two equations

Line 1: \(y =-\frac{1}{2}x - 2\).
Line 2 (after rewriting): \(y=-\frac{1}{2}x - 2\).
Since the two equations are identical (\(a_1=a_2\), \(b_1 = b_2\), \(c_1=c_2\) where \(a\), \(b\), \(c\) are coefficients of \(ax+by = c\)).

Answer:

• The system of equations is: consistent dependent.
• This means the system has: infinitely many solutions.